@Seedfork
The researchers wrote "Time of floral initiation in Hemerocallis cultivars was correlated to the blooming period."
That is formally the correct description. However, daylilies are classified by when they bloom and they cannot be classified by when they initiate their scapes as that can only be determined by microscopic examination of dissected and sectioned tissues. It is not known.
The other aspect of when a daylily flowers is that the first flowering will tend to be unusual in timing. It may not even happen at the usual time for the particular daylily. In those locations where daylilies rarely rebloom the timing between the second bloom period and the third period will tend to be more or less the same as that between all later consecutive bloom periods.
What happens to the timing in those locations and conditions where daylilies may flower and then rebloom once or twice or three times in the same growing season would be interesting to examine.
Yes, daylilies will have an inherited blooming season. The factors that are part of the inheritance of the characteristic blooming season in daylilies are not known but the growth rate, how a daylily responds to temperature, fertilizer, etc. and how large the crown (or perhaps more precisely the growing point - shoot apical meristem) must be, are probably all factors.